Question

For the below function,

I did

But I must have did wrong … answer should be O(log n). I am terrible at Big O … havent fully understood master theorem which is not taught in school yet. They taught only recursion tree

Answer 1

If we suppose that all arithmetic operations are done in O(1) then:
As we see each function call we divide exp on 2. When we reach zero with exp – we done.
How many times we can divide exp on two without reaching zero? That’s log exp. So the log exp function calls * O(1) gives log(exp) complexity.
Finding sum of geometric sequence you finding answer to another problem: how many node in complete (where all siblings exist) tree with n leaves:
suppose n = 4:

1'
|_1''
  |_1'''
  |_2'''
|_2''
  |_3'''
  |_4'''

you are finding count of node in such a tree